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Classification of datasets with imputed missing values: does imputation quality matter?

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arXiv 2022年

作者： Shadbahr, Tolou Roberts, Michael Stanczuk, Jan Gilbey, Julian Teare, Philip Dittmer, Sören Thorpe, Matthew Torné, Ramon Viñas Sala, Evis Lió, Pietro Patel, Mishal Rudd, James H.F. Mirtti, Tuomas Rannikko, Antti Sakari Aston, John A.D. Tang, Jing Schönlieb, Carola-Bibiane Selby, Ian Breger, Anna Weir-McCall, Jonathan R. Gkrania-Klotsas, Effrossyni Korhonen, Anna Jefferson, Emily Langs, Georg Yang, Guang Prosch, Helmut Preller, Jacobus Stanczuk, Jan Babar, Judith Sánchez, Lorena Escudero Wassin, Marcel Holzer, Markus Walton, Nicholas Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence AstraZeneca Cambridge United Kingdom Department of Mathematics University of Manchester Manchester United Kingdom Department of Computer Science and Technology University of Cambridge Cambridge United Kingdom Department of Radiology University of Cambridge Cambridge United Kingdom Clinical Pharmacology & Safety Sciences AstraZeneca Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pathology University of Helsinki Helsinki University Hospital Finland iCAN-Digital Precision Cancer Medicine Flagship Helsinki Finland Department of Urology University of Helsinki Helsinki University Hospital Helsinki Finland Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Faculty of Mathematics University of Vienna Austria Royal Papworth Hospital Cambridge Royal Papworth Hospital NHS Foundation Trust Cambridge United Kingdom Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Language Technology Laboratory University of Cambridge Cambridge United Kingdom Population Health and Genomics School of Medicine University of Dundee Dundee United Kingdom Department of Biomedical Imaging and Image-guided Therapy Computational Imaging Research Lab Medical University of Vienna Vienna Austria National Heart and Lung Institute Imperial College London London United Kingdom Contextflow GmbH Vienna Austria Institute of Astronomy University of Cambridge Cambridge United Kingdom

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data. All code and data used in this paper are also released publicly at [inserted upon publication]. © 2022, CC BY.

关键词： Classification (of information)

Deep learning inter-atomic potential model for accurate irradiation damage simulationsa)

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arXiv 2019年

作者： Wang, Hao Guo, Xun Zhang, Linfeng Wang, Han Xue, Jianming State Key Laboratory of Nuclear Physics and Technology School of Physics CAPT HEDPS IFSA Collaborative Innovation Center of MoE College of Engineering Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100871 China State Key Laboratory of Nuclear Physics and Technology School of Physics CAPT HEDPS IFSA Collaborative Innovation Center of MoE College of Engineering Peking University Beijing100871 China

We propose a hybrid scheme that interpolates smoothly the Ziegler-Biersack-Littmark (ZBL) screened nuclear repulsion potential with a newly developed deep learning potential energy model. The resulting DP-ZBL model can not only provide overall good performance on the predictions of near-equilibrium material properties but also capture the right physics when atoms are extremely close to each other, an event that frequently happens in computational simulations of irradiation damage events. We applied this scheme to the simulation of the irradiation damage processes in the face-centered-cubic aluminium system, and found better descriptions in terms of the defect formation energy, evolution of collision cascades, displacement threshold energy, and residual point defects, than the widely-adopted ZBL modified embedded atom method potentials and its variants. Our work provides a reliable and feasible scheme to accurately simulate the irradiation damage processes and opens up new opportunities to solve the predicament of lacking accurate potentials for enormous newly-discovered materials in the irradiation effect field. Copyright © 2019, The Authors. All rights reserved.

关键词： Potential energy

Methodology to construct large realizations of perfectly hyperuniform disordered packings

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Physical Review E 2019年第5期99卷 052141-052141页

作者： Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Disordered hyperuniform packings (or dispersions) are unusual amorphous two-phase materials that are endowed with exotic physical properties. Such hyperuniform systems are characterized by an anomalous suppression of volume-fraction fluctuations at infinitely long-wavelengths, compared to ordinary disordered materials. While there has been growing interest in such singular states of amorphous matter, a major obstacle has been an inability to produce large samples that are perfectly hyperuniform due to practical limitations of conventional numerical and experimental methods. To overcome these limitations, we introduce a general theoretical methodology to construct perfectly hyperuniform packings in d-dimensional Euclidean space Rd. Specifically, beginning with an initial general tessellation of space by disjoint cells that meets a “bounded-cell” condition, hard particles of general shape are placed inside each cell such that the local-cell particle packing fractions are identical to the global packing fraction. We prove that the constructed packings with a polydispersity in size are perfectly hyperuniform in the infinite-sample-size limit, regardless of particle shapes, positions, and numbers per cell. We use this theoretical formulation to devise an efficient and tunable algorithm to generate extremely large realizations of such packings. We employ two distinct initial tessellations: Voronoi as well as sphere tessellations. Beginning with Voronoi tessellations, we show that our algorithm can remarkably convert extremely large nonhyperuniform packings into hyperuniform ones in R2 and R3. Implementing our theoretical methodology on sphere tessellations, we establish the hyperuniformity of the classical Hashin-Shtrikman multiscale coated-spheres structures, which are known to be two-phase media microstructures that possess optimal effective transport and elastic properties. A consequence of our work is a rigorous demonstration that packings that have identical tessella

关键词： Fluctuations & noise

End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 18

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End-to-end symmetry preserving inter-atomic potential energy...

Proceedings of the 32nd International Conference on Neural Information Processing Systems

作者： Linfeng Zhang Jiequn Han Han Wang Wissam A. Saidi Roberto Car E. Weinan Program in Applied and Computational Mathematics Princeton University Institute of Applied Physics and Computational Mathematics China and CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh Program in Applied and Computational Mathematics Princeton University and Department of Chemistry and Department of Physics Princeton University and Princeton Institute for the Science and Technology of Materials Princeton University Program in Applied and Computational Mathematics Princeton University and Department of Mathematics Princeton University and Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity.

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Isotope effects in liquid water via deep potential molecular dynamics

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arXiv 2019年

作者： Ko, Hsin-Yu Zhang, Linfeng Santra, Biswajit Wang, Han Weinan, E. DiStasio, Robert A. Cara, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry and Chemical Biology Cornell University IthacaNY14853 United States Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model - a neural-network representation of the ab initio PES - in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H2O and D2O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

Universal approximation of symmetric and anti-symmetric functions

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arXiv 2019年

作者： Han, Jiequn Li, Yingzhou Lin, Lin Lu, Jianfeng Zhang, Jiefu Zhang, Linfeng Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics Department of Physics Department of Chemistry Duke University DurhamNC27708 United States Department of Mathematics University of California BerkeleyCA94720 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy ǫ. While the approximation still suffers from curse of dimensionality, to the best of our knowledge, these are first results in the literature with explicit error bounds. Moreover, we also discuss neural network architecture that can be suitable for approximating symmetric and anti-symmetric functions. Copyright © 2019, The Authors. All rights reserved.

关键词： Network architecture

End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 32

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End-to-end symmetry preserving inter-atomic potential energy...

32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Zhang, Linfeng Han, Jiequn Wang, Han Saidi, Wissam A. Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Institute of Applied Physics and Computational Mathematics China CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh United States Department of Chemistry Department of Physics Princeton University United States Princeton Institute for the Science and Technology of Materials Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China

关键词： Potential energy

Manifold learning-based methods for analyzing single-cell RNA-sequencing data

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Current Opinion in Systems Biology 2018年 7卷 36-46页

作者： Moon, Kevin R. Stanley, Jay S. Burkhardt, Daniel van Dijk, David Wolf, Guy Krishnaswamy, Smita Department of Genetics Yale University New Haven CT United States Applied Mathematics Program Yale University New Haven CT United States Computational Biology and Bioinformatics Program Yale University New Haven CT United States Department of Computer Science Yale University New Haven CT United States

Recent advances in single-cell RNA sequencing technologies enable deep insights into cellular development, gene regulation, and phenotypic diversity by measuring gene expression for thousands of cells in a single experiment. While these technologies hold great potential for improving our understanding of cellular states and progression, they also pose new challenges and require advanced mathematical and algorithmic tools to extract underlying biological signals. In this review, we cover one of the most promising avenues of research into unlocking the potential of scRNA-seq data: the field of manifold learning, and the related manifold assumption in data analysis. Manifold learning provides a powerful structure for algorithmic approaches to process the data, extract its dynamics, and infer patterns in it. In particular, we cover manifold learning-based methods for denoising the data, revealing gene interactions, extracting pseudotime progressions with model fitting, visualizing the cellular state space via dimensionality reduction, and clustering the data. © 2017 Published by Elsevier Ltd.

关键词： Data mining Gene regulatory networks Imputation Manifold learning Pseudotime trends Single cell RNA sequencing

Geometry based data generation 32

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Geometry based data generation

32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Lindenbaum, Ofir Wolf, Guy Stanley, Jay S. Krishnaswamy, Smita Applied Mathematics Program Yale University New HavenCT06511 United States Computational Biology and Bioinformatics Program Yale University New HavenCT06510 United States Departments of Genetics and Computer Science Yale University New HavenCT06510 United States

We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold. This is in contrast to existing generative models that represent data density, and are strongly affected by noise and other artifacts of data collection. We demonstrate how this approach corrects sampling biases and artifacts, thus improves several downstream data analysis tasks, such as clustering and classification. Finally, we demonstrate that this approach is especially useful in biology where, despite the advent of single-cell technologies, rare subpopulations and gene-interaction relationships are affected by biased sampling. We show that SUGAR can generate hypothetical populations, and it is able to reveal intrinsic patterns and mutual-information relationships between genes on a single-cell RNA sequencing dataset of hematopoiesis. © 2018 Curran Associates Inc..All rights reserved.

关键词： Genes